F.3 MATHS - Ans.fyi 參考答案

F.3 MATHS

2009-06-28 6:23 pm

1.(a)
cosθtanθ

(b)
4- 4cos^2θ

(c)
sin^2θ/2tanθ

(d)
sinθ/sin(90º - θ)

2. If tanθ=4, find the values of
(a) 2cosθ/3sinθ

(b) 3sinθ- 4cosθ/2cosθ

3. Find the value of θ.
(a) (√3)sinθ= cosθ

(b) 2cos3θ= 1

4. If sinθ=2/5, find cosθ and tanθ(leave the answers in surd form)

回答 (1)

用戶10012

2009-06-28 7:29 pm

✔ 最佳答案

1a. = cos x ( sin x/cos x) = sin x.
1b.
4 - 4 cos ^2 x = 4(1 - cos ^2 x ) = 4 sin ^2 x.
1c.
= sin ^2 x /2(sin x/cos x) = sin x cos x/2.
1d.
= sin x /cos x = tan x.
2.
a. 2 cos x /3 sin x = 2/3tan x = 2/(3 x 4 ) = 2/12 = 1/6.
b. = 3 sin x/2 cos x - 4 cos x /2 cos x = 3 tan x/2 - 2 = 12/2 - 2 = 6- 2 = 4.
3a.
tan x = 1/sqrt 3 = tan 30
so x = 30 degree.
3b.
cos 3x = 1/2 = cos 60
so 3x = 60
x = 20 degree.
4.
sin x = 2/5. By Pythagoras theorem, tan x = 2/sqrt(5^2 - 2^2)
= 2/sqrt(25 - 4) = 2/sqrt21= 2sqrt21/(21).
cos x = sqrt21/5.

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